Extended Nielsen transformations and triviality of a group
type: Item
instance of: scholarly article
title: Extended Nielsen transformations and triviality of a group
zbMATH Open document ID: 0573.20029
DOI: 10.1007/BF01139985
published in: Mathematical Notes
publication date: 1984-01-01T00:00:00Z
review text: It was conjectured by \textit{J. J. Andrews} and \textit{M. L. Curtis} [Proc. Am. Math. Soc. 16, 192-195 (1965; Zbl 0131.38301) and Am. Math. Mon. 73, 21-28 (1966; Zbl 0135.044)] that if the trivial group has a finite balanced presentation \(<x_ 1,...,x_ n|\) \(r_ 1,...,r_ n>\) then \(\{r_ 1,...,r_ n\}\) can be transformed into \(\{x_ 1,...,x_ n\}\) by a sequence of transformations each of which is either an elementary Nielsen transformation or else consists of replacing some element by a conjugate. The author gives a proof of this conjecture in the variety of solvable groups.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 55Q99
Mathematics Subject Classification ID: 20F38
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 3914562
zbMATH Keywords: Andrews-Curtis problem
zbMATH Keywords: trivial group
zbMATH Keywords: finite balanced presentation
zbMATH Keywords: elementary Nielsen transformation
zbMATH Keywords: solvable groups
author: Alexei Myasnikov
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
cites work: Extended Nielsen Operations in Free Groups
cites work: Free Heegaard diagrams and extended Nielsen transformations. II
full work available at URL: https://doi.org/10.1007/bf01139985
OpenAlex ID: W2021171927
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description: scientific article; zbMATH DE number 3914562